Bond and Percent
Bond P is a premium bond with a 12 percent coupon. Bond D is a 6 percent coupon bond currently selling at a discount. Both bonds make annual payments, have a YTM of 9 percent, and have five years to maturity. The current yield for Bonds P and D is percent and percent, respectively. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16)) | If interest rates remain unchanged, the expected capital gains yield over the next year for Bonds P and D is percent and percent, respectively. (Do not include the percent signs (%). Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16)) |
Explanation: To find the capital gains yield and the current yield, we need to find the price of the bond. The current price of Bond P and the price of Bond P in one year is: | P: | P0 = $120(PVIFA9%,5) + $1,000(PVIF9%,5) = $1,116.69 | | | | P1 = $120(PVIFA9%,4) + $1,000(PVIF9%,4) = $1,097.19 | | | | Current yield = $120 / $1,116.69 = .1075 or 10.75% | | | | The capital gains yield is: | | | | Capital gains yield = (New price – Original price) / Original price | | | | Capital gains yield = ($1,097.19 – 1,111.69) / $1,116.69 = –.0175 or –1.75% | | | | The current price of Bond D and the price of Bond D in one year is: | D: | P0 = $60(PVIFA9%,5) + $1,000(PVIF9%,5) = $883.31 | | | | P1 = $60(PVIFA9%,4) + $1,000(PVIF9%,4) = $902.81 | | | | Current yield = $60 / $883.81 = .0679 or 6.79% | | | | Capital gains yield = ($902.81 – 883.31) / $883.31 = +.0221 or +2.21% | All else held constant, premium bonds pay high current income while having price depreciation as maturity nears; discount bonds do not pay high current income but have price appreciation as maturity nears. For either bond, the total return is still 9%, but this return is distributed differently between current income and capital
Explanation: To find the capital gains yield and the current yield, we need to find the price of the bond. The current price of Bond P and the price of Bond P in one year is: | P: | P0 = $120(PVIFA9%,5) + $1,000(PVIF9%,5) = $1,116.69 | | | | P1 = $120(PVIFA9%,4) + $1,000(PVIF9%,4) = $1,097.19 | | | | Current yield = $120 / $1,116.69 = .1075 or 10.75% | | | | The capital gains yield is: | | | | Capital gains yield = (New price – Original price) / Original price | | | | Capital gains yield = ($1,097.19 – 1,111.69) / $1,116.69 = –.0175 or –1.75% | | | | The current price of Bond D and the price of Bond D in one year is: | D: | P0 = $60(PVIFA9%,5) + $1,000(PVIF9%,5) = $883.31 | | | | P1 = $60(PVIFA9%,4) + $1,000(PVIF9%,4) = $902.81 | | | | Current yield = $60 / $883.81 = .0679 or 6.79% | | | | Capital gains yield = ($902.81 – 883.31) / $883.31 = +.0221 or +2.21% | All else held constant, premium bonds pay high current income while having price depreciation as maturity nears; discount bonds do not pay high current income but have price appreciation as maturity nears. For either bond, the total return is still 9%, but this return is distributed differently between current income and capital